Michael , Silberstein (2011) *Relational Blockworld: A Path Integral Based Interpretation of Quantum Field Theory.* In: [2010] Philosophy of Science Assoc. 22nd Biennial Mtg (Montréal, QC) > PSA 2010 Contributed Papers.

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## Abstract

We propose a new path integral based interpretation of quantum field theory (QFT). In

our interpretation, QFT is the continuous approximation of a more fundamental, discrete

graph theory (theory X) whereby the transition amplitude Z is not viewed as a sum over

all paths in configuration space, but measures the symmetry of the differential operator

and source vector of the discrete graphical action. We propose that the differential

operator and source vector of theory X are related via a self-consistency criterion (SCC)

based on the identity that underwrites divergence-free sources in classical field theory,

i.e., the boundary of a boundary principle. In this approach, the SCC ensures the source

vector is divergence-free and resides in the row space of the differential operator.

Accordingly, the differential operator will necessarily have a non-trivial eigenvector with

eigenvalue zero, so the SCC is the origin of gauge invariance. Factors of infinity

associated with gauge groups of infinite volume are excluded in our approach, since Z is

restricted to the row space of the differential operator and source vector. We show it is

possible that the underlying theory X, despite being discrete, is the basis for exact

Poincaré invariance. Using this formalism, we obtain the two-source transition amplitude

over a (1+1)-dimensional graph with N vertices fundamental to the scalar Gaussian

theory and interpret it in the context of the twin-slit experiment to provide a unified

account of the Aharonov-Bohm effect and quantum non-separability (superposition and

entanglement) that illustrates our ontic structural realist alternative to problematic particle

and field ontologies. Our account also explains the need for regularization and

renormalization, explains gauge invariance and largely discharges the problems of

inequivalent representations and Haag’s theorem. This view suggests corrections to

general relativity via modifications to its graphical counterpart, Regge calculus. We

conclude by presenting the results of our modified Regge calculus approach to Einsteinde

Sitter cosmology where we produced a fit to the Union2 Compilation data for type Ia

supernovae rivaling that of the concordance model (ΛCDM), but without having to

invoke dark energy or accelerated expansion.

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Item Type: | Conference or Workshop Item (UNSPECIFIED) |
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Keywords: | quantum field theory, path integral, renormalization |

Subjects: | Specific Sciences > Physics Specific Sciences > Physics > Quantum Field Theory |

Conferences and Volumes: | [2010] Philosophy of Science Assoc. 22nd Biennial Mtg (Montréal, QC) > PSA 2010 Contributed Papers |

Depositing User: | Michael Silberstein |

Date Deposited: | 20 Oct 2011 07:31 |

Last Modified: | 20 Oct 2011 07:31 |

Item ID: | 8851 |

URI: | http://philsci-archive.pitt.edu/id/eprint/8851 |

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